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Motor Drive Unit Component

This is a model of motor drive unit (MDU), which is a system consisting of an electric motor and a controller. This MDU model is abstract and simulates the high-level behavior of power conversion between electric and mechanical powers by considering power conversion efficiency or losses.

Models

The core system equations of the MDU model are generally as follows.

J * dw/dt = trq_rot + trq_cmd - k_f * w
Power_mech = trq_cmd * w
Power_elec = i * V
Power_elec = Power_mech + P_elecloss
Power_elecloss = Power_copper + Power_iron + Power_fixed
Power_copper = k_c * (trq_rot)^2
Power_iron = k_i * w^2
Mass_therm * d(T_mdu)/dt = Power_elecloss + Q_input

where

  • J ... motor inertia (parameter)
  • t ... time (independent variable)
  • w ... rotor angular speed (state)
  • trq_rot ... torque at motor rotor
  • trq_cmd ... torque command input to MDU
  • k_f ... rotor frictional damping coefficient (parameter)
  • Power_mech ... mechanical power (intermediate variable)
  • Power_elec ... electrical power (intermediate variable). The sign indicates if the system is generating or consuming electric power.
  • Power_elecloss ... electrical losses (parameter). This can be modelled as a scalar constant, a formula as a function of motor speed etc., or a tabulated map.
  • i ... electric current (connected to DC power supply)
  • V ... voltage drop (connected to DC power supply)
  • Power_copper ... copper loss
  • Power_iron ... iron loss
  • Power_fixed ... fixed loss which is constant across the whole operating region (parameter)
  • k_c ... copper loss coefficient (parameter)
  • k_i ... iron loss coefficient (parameter)
  • Mass_therm ... thermal mass of MDU (parameter)
  • T_mdu ... temperature of MDU (state)
  • Q_input ... heat flow rate input to MDU

In the models below (except for System-level model with tabulated losses), copper loss coefficient k_c is deteremined using the single efficiency measurement model

k_c = w_meas * (1 - eff_meas) / (trq_meas * eff_meas)

where

  • eff_meas ... measured efficiency (normalized between 0 and 1)
  • w_meas ... motor speed at which efficiency is measured
  • trq_meas ... torque at which efficiecy is measured

Iron loss coefficient k_i depends on the characteristics of motor drive unit, but it could be typically about 10% of k_c.

This component provides the following four models based on the above formulation. These models are highly abstract and run fast.

Basic model (MotorDriveUnit_refsub_Basic) is the simplest model with the fewest parameters among the four models. It uses Motor & Drive block from Simscape Driveline. This model takes torque command and computes power conversion between electrical and mechanical powers using the single efficiency measurement model to compute copper loss coefficient k_c. Irons loss Power_iron and fixed loss Power_fixed are not modeled. This model does not simulate temperature dynamics. Below is an example plot of efficiency contour of the Basic model.

Efficiency contour plot of the basic model of motor drive unit

Basic thermal model (MotorDriveUnit_refsub_BasicThermal) uses Motor & Drive block, which is the same block as the above Basic model uses, but with thermal model enabled to simulate motor temperature dynamics.

System-level model (MotorDriveUnit_refsub_System) uses Motor & Drive (System-Level) block from Simscape Electrical to compute power conversion between electrical and mechanical powers. Thermal model is enabled too. Power conversion model is the same as the one in Basic and Basic thermal models above, i.e., the single efficiency measurement model, but irons loss Power_iron and fixed loss Power_fixed are also considered in this model. Below is an example plot of efficiency contour of the System-level model.

Efficiency contour plot of the basic model of motor drive unit

System-level model with tabulated losses (MotorDriveUnit_refsub_SystemTable) uses Motor & Drive (System-Level) block from Simscape Electrical. It takes torque command and computes motor speed which is the same as the other models above, but for power conversion efficiency or losses, this model uses tabulated parameter data as a function of motor speed and torque Power(trq_rot, w) instead of the single efficiency measurement model. Thermal model is disabled, but you can enable it if you have two data sets of efficiency or losses measured at two different temperatures.

Harness model

To run simulation with the above models, use a harness model in Harness folder.

  • MotorDriveUnit_harness_model.mdl

You can select the model using buttons in Configuration block.

Simulation Cases

SimulationCases folder contains Live Scripts that are used to visually inspect the simulation behaviors of the models in various simulation scenarios as follows.

  • Constant ... All inputs are constant. This is used to check that the harness model runs.

  • Drive ... MDU drives axle by consuming electric power.

  • Regenerative braking ... Axle drives motor, and MDU generates electric power.

  • Random .... Input signals for motor torque command and axle load torque are randomly generated.

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